Remember Newton's laws: an object only accelerates when it has a force acting on it. If you're in free space and you throw and object, you are essentially releasing it at a constant velocity. After this, no force acts on the object and so it will continue to travel at a constant velocity forever. It will not speed up!
If, on the other hand, you find a way to apply a constant force to it, it will be seen to accelerate. However, while its velocity will increase, it will never cross (or even reach) the speed of light in any finite amount of time. This is fundamentally due to the way that velocities add in special relativity, which is different from our "common-sense" way of looking at things. See this answer for the exact formula. You may also find this answer to a different (but similar) question interesting.